Depth-dependent mud density determination and processing for horizontal shear slowness in vertical transverse isotropy environment using full-waveform sonic data

ABSTRACT

An acoustic logging method that may comprise acquiring waveforms for multiple acoustic wave modes as a function of tool position in a borehole; deriving position-dependent mode dispersion curves from the waveforms; accessing a computed library of dispersion curves for a vertical shear slowness (s) and a Thomsen gamma (γ) of a given acoustic wave mode as a function of frequency; interpolating dispersion curves in the computed library to an assumed known compressional wave slowness, a borehole radius, a formation density, a mud density, and a mud slowness; computing an adaptive weight; and inverting dispersion curve modes jointly for a shear wave anisotropy, a vertical shear wave slowness, an inverted mud slowness, and an inverted mud density as a function of depth. An acoustic logging system may comprise a logging tool, a conveyance attached to the logging tool, at least one sensor, and at least one processor.

BACKGROUND

During oil and gas exploration, many types of information may becollected and analyzed. The information may be used to determine thequantity and quality of hydrocarbons in a reservoir and to develop ormodify strategies for hydrocarbon production. For instance, theinformation may be used for reservoir evaluation, flow assurance,reservoir stimulation, facility enhancement, production enhancementstrategies, and reserve estimation. Resistivity, density, and porositylogs have proven to be particularly useful for determining the locationof hydrocarbon gases and fluids. One technique for collecting relevantinformation may be acoustic logging. Acoustic logging tools providemeasurements of acoustic wave propagation speeds through the formation.There are multiple wave propagation modes that can be measured,including compressional and flexural. Taken together, the propagationspeeds of these various modes often indicate formation density andporosity.

Acoustic logging measurements are also valuable for determining thevelocity structure of subsurface formations, which information is usefulfor migrating seismic survey data to obtain accurate images of thesubsurface formation structure. Subsurface formations are oftenanisotropic, meaning that the acoustic wave's propagation speed dependson the direction in which the wave propagates. Most often theformations, even when anisotropic, are relatively isotropic in thehorizontal plane. This particular version of anisotropy is often calledvertical transverse isotropy (VTI). Accurate imaging requires that suchanisotropy be accounted for during the migration process. Whensufficiently precise, such imaging enables reservoirs to be delineatedfrom surrounding formations, and further indicates the presence offormation boundaries, laminations, and fractures, which information isdesired by an operator as they formulate a production strategy thatmaximizes the reservoir's economic value. However, inversion of thesemeasurements for VTI anisotropy is sensitive to mud slowness and muddensity in a wellbore. Even a small error in these wellbore parametersmay result in large anisotropy estimation errors.

BRIEF DESCRIPTION OF THE DRAWINGS

These drawings illustrate certain aspects of some of the embodiments ofthe present disclosure, and should not be used to limit or define thedisclosure;

FIG. 1 shows an illustrative logging-while-drilling (LWD) environment;

FIG. 2 shows an illustrative wireline logging environment;

FIG. 3A shows an illustrative acoustic logging tool;

FIG. 3B shows an illustrative receiver having azimuthal sensitivity;

FIG. 4 shows illustrative receive waveforms;

FIG. 5 is a functional block diagram of illustrative tool electronics;

FIG. 6 shows an illustrative system for implementing methods disclosedherein;

FIG. 7 is a graph illustrating the identification of mud slowness;

FIG. 8 is a graph illustrating mud slowness in view of depth;

FIG. 9 is a graph of measurements from a drilling fluid sample;

FIGS. 10A and 10B are graphs illustrating an inverted Gamma anisotropyparameter with surface mud density measurements;

FIGS. 11A and 11B are graphs illustrating an inverted Gamma anisotropyparameter in an upper section;

FIG. 12 is an inversion workflow for both mud slowness and mud density;

FIG. 13 is a graph of a two-dimensional objective function frominverting for the mud slowness and the mud density;

FIG. 14 is a workflow to reduce the computational burden for invertingthe mud slowness and the mud density;

FIG. 15 is a graph from the workflow in FIG. 14; and

FIG. 16 is a graph of a regression analysis relationship between the mudslowness and the mud density.

DETAILED DESCRIPTION

Accurate anisotropy measurements may improve seismic-well measurements.Determination of mud density as a function of depth may also provideinformation to an operator and may improve the accuracy of any algorithmthat may use borehole fluid density as an input. Proper measurements maybe taken with logging devices which may be found in a conveyance and/orbottom hole assembly.

Accordingly, FIG. 1 shows an illustrative logging while drilling (LWD)environment. A drilling platform 2 is equipped with a derrick 4 thatsupports a hoist 6. The rig operator drills an oil or gas well using adrill string 8 of multiple concentric drill pipes. The hoist 6 suspendsa top drive 10 that rotates the drill string 8 as it lowers the drillstring through the wellhead 12. Connected to the lower end of the drillstring 8 is a drill bit 14. The drill bit 14 is rotated and drillingaccomplished by rotating the drill string 8, by use of a downhole motornear the drill bit, or by both methods. Recirculation equipment 16 pumpsdrilling fluid through supply pipe 18, through top drive 10, and downthrough the drill string 8 at high pressures and volumes to emergethrough nozzles or jets in the drill bit 14. The drilling fluid thentravels back up the hole via the annulus formed between the exterior ofthe drill string 8 and the borehole wall 20, through a blowoutpreventer, and into a retention pit 22 on the surface. On the surface,the drilling fluid is cleaned and then recirculated by recirculationequipment 16. The drilling fluid carries cuttings from the base of thebore to the surface and balances the hydrostatic pressure in the rockformations.

The bottomhole assembly (i.e., the lowermost part of drill string 8)includes thick-walled tubulars called drill collars, which add weightand rigidity to aid the drilling process. The thick walls of these drillcollars make them useful for housing instrumentation and LWD sensors.Thus, for example, the bottomhole assembly of FIG. 1 includes a naturalgamma ray detector 24, a resistivity tool 28, an acoustic logging tool26, a neutron porosity tool 30, and a control & telemetry module 32.Other tools and sensors can also be included in the bottomhole assembly,including position sensors, orientation sensors, pressure sensors,temperature sensors, vibration sensors, etc. From the various bottomholeassembly sensors, the control and telemetry module 32 collects dataregarding the formation properties and/or various drilling parametersand stores the data in internal memory. In addition, some or all of thedata is transmitted to the surface by, e.g., mud pulse telemetry.

Telemetry module 32 modulates a resistance to drilling fluid flow togenerate pressure pulses that propagate to the surface. One or morepressure transducers 34, 36 (isolated from the noise of therecirculation equipment 16 by a desurger 40) convert the pressure signalinto electrical signal(s) for a signal digitizer 38. The signaldigitizer 38 supplies a digital form of the pressure signals to acomputer 50 or some other form of a data processing device. Computer 50operates in accordance with software (which may be stored on informationstorage media 52) and user input received via an input device 54 toprocess and decode the received signals. The resulting telemetry datamay be further analyzed and processed by computer 50 to generate adisplay of useful information on a computer monitor 56 or some otherform of a display device. For example, a driller could employ thissystem to obtain and view an acoustic slowness and anisotropy log.

At various times during the drilling process, the drill string 8 may beremoved from the borehole as shown in FIG. 2. Once the drill string hasbeen removed, logging operations can be conducted using a wirelinelogging tool 62, i.e., a sensing instrument sonde suspended by a cable66 having conductors for transporting power to the tool and telemetryfrom the tool to the surface. The wireline tool assembly can include anacoustic logging tool similar to the LWD embodiment described hereinbelow. Other formation property sensors may additionally oralternatively be included to measure formation properties as the tool ispulled uphole. A logging facility 68 collects measurements from thewireline logging tool 62 and includes computing facilities forprocessing and storing the measurements gathered by the logging tool.

FIG. 3A shows an illustrative embodiment of an acoustic logging tool 26disposed proximate a borehole wall 20. The acoustic logging tool 26includes a monopole acoustic source 72, an acoustic isolator 74, areceiver array 76, and a multi-pole source 80. The multi-pole source 80may be a dipole, crossed-dipole, quadrupole, hexapole, or higher-ordermulti-pole transmitter. Some tool embodiments may include one acousticsource that is configurable to generate different wave modes rather thanhaving separate transmitter sources, but in each case the source(s) aredesigned to generate acoustic waves 78 that propagate through theformation and are detected by the receiver array 76. The acoustic source(e.g., the monopole acoustic source 72, multi-pole source 80, or both)may be made up of piezoelectric elements, bender bars, or othertransducers suitable for generating acoustic waves in downholeconditions. The contemplated operating frequencies for the acousticlogging tool 26 are in the range between 0.5 kHz and 30 kHz, inclusive.The operating frequency may be selected based on a tradeoff betweenattenuation and wavelength in which the wavelength is minimized subjectto requirements for limited attenuation. Subject to the attenuationlimits on performance, smaller wavelengths may offer improved spatialresolution of the tool.

The acoustic isolator 74 serves to attenuate and delay acoustic wavesthat propagate through the body of the tool from the monopole acousticsource 72 to the receiver array 76. Any standard acoustic isolator maybe used. Receiver array 76 may include multiple sectorized receiversspaced apart along the axis of the tool. (One such sectorized receiver58 is illustrated in cross-section in FIG. 3B). Although five receiversare shown in FIG. 3A, the number may vary from one to sixteen or more.Each sectorized receiver 58 includes a number of azimuthally spacedsectors. Referring to FIG. 3B, a sectorized receiver 58 having eightsectors A1-A8 is shown. However, the number of sectors may vary and ispreferably (but not necessarily) in the range between 4 and 16,inclusive. Each sector may include a piezoelectric element that convertsacoustic waves into an electrical signal that is amplified and convertedto a digital signal. The digital signal from each sector is individuallymeasured by an internal controller for processing, storage, and/ortransmission to an uphole computing facility. Though the individualsectors may be calibrated to match their responses, such calibrationsmay vary differently for each sector as a function of temperature,pressure, and other environmental factors. Accordingly, in at least someembodiments, the individual sectors may be machined from a cylindrical(or conical) transducer. In this fashion, it may ensure that each of thereceiver sectors may have matching characteristics.

When the acoustic logging tool 26 is enabled, the internal controllercontrols the triggering and timing of the monopole acoustic source 72and/or multi-pole source 80, and records and processes the signals fromthe receiver array 76. The internal controller fires the monopoleacoustic source 72 periodically, producing acoustic pressure waves thatpropagate through the fluid in borehole wall 20 and into the surroundingformation. As these pressure waves propagate past the receiver array 76,they cause pressure variations that can be detected by the receiverarray elements.

The receiver array signals may be processed by the internal controllerto determine the true formation anisotropy and shear velocity, or thesignals may be communicated to the uphole computer system forprocessing. The measurements are associated with borehole position (andpossibly tool orientation) to generate a log or image of the acousticalproperties of the borehole. The log or image may be stored andultimately displayed for viewing by an operator.

FIG. 4 shows a set of illustrative amplitude versus time waveforms 82detected by the receiver array 76 in response to one triggering of themonopole acoustic source 72 and/or multi-pole source 80. The receiversmay be located at about 3 ft. (about 1 meter), about 3.5 ft. (about 1meter), about 4 ft. (about 1.25 meter), about 4.5 ft. (about 1.25meters) and about 5 ft. (1.5 meters) from the monopole acoustic source72, and various slowness value slopes are shown to aid interpretation.The time scale is from about 80 μs to about 1500 μs. Each of thewaveforms is shown for a corresponding receiver as a function of timesince the transmitter firing. (Note the increased time delay before theacoustic waves reach the increasingly distant receivers.) Afterrecording the waveforms, the internal controller typically normalizesthe waveforms so that they have the same signal energy.

The detected waveforms represent multiple waves, including wavespropagating through the body of the tool (“tool waves”), compressionwaves from the formation, shear waves from the formation, wavespropagating through the borehole fluid (“mud waves”), and Stoneley wavespropagating along the borehole wall. Each wave type has a differentpropagation velocity which separates them from each other and enablestheir velocities to be independently measured.

The receiver array signals may be processed by a downhole controller todetermine V_(S) (the formation shear wave velocity) and V_(C) (theformation compression wave velocity), or the signals may be communicatedto the uphole computer system for processing. (Though the term“velocity” is commonly used, the measured value is normally a scalarvalue, i.e., the speed. The speed (velocity) may also be equivalentlyexpressed in terms of slowness, which is the reciprocal of speed.) Whenthe velocity is determined as a function of frequency, the velocity maybe termed a “dispersion curve”, as the variation of velocity withfrequency causes the wave energy to spread out as it propagates.

The acoustic velocity measurements are associated with borehole position(and possibly tool orientation) to generate a log or image of theacoustical properties of the borehole. The log or image is stored andultimately displayed for viewing by a user.

The illustrative acoustic logging tool 26 may further include a fluidcell to measure acoustic properties of the borehole fluid. Specifically,the fluid cell measures V_(M), the velocity of compression waves in theborehole fluid and ρ_(M), the density of the borehole fluid.Alternatively, the acoustic impedance Z_(M)=ρ_(M)V_(M) may be measured.The fluid cell can be operated in a manner that avoids interference fromfirings of the monopole acoustic source 72, e.g., the borehole fluidproperty measurements may be made while the monopole acoustic source 72is quiet, and the formation wave velocity measurements may be made whilethe fluid cell is quiet. Alternatively, the acoustic properties of theborehole fluid may be measured at the surface and subjected tocorrections for compensate for temperature and pressure variation.

FIG. 5 is a functional block diagram of the illustrative acousticlogging tool 26. A digital signal processor 102 operates as an internalcontroller for acoustic logging tool 26 by executing software stored inmemory 104. The software configures the digital signal processor 102 tocollect measurements from various measurement modules such as positionsensor 106 and fluid cell 108. (Note that these modules canalternatively be implemented as separate tools in a wireline sonde orbottomhole assembly, in which case such measurements would be gatheredby a control/telemetry module.)

The software further configures the digital signal processor 102 to firethe monopole acoustic source(s) 72 via a digital to analog converter112, and further configures the digital signal processor 102 to obtainreceive waveforms from receiver array 76 via analog to digitalconverters 116-120. The digitized waveforms may be stored in memory 104and/or processed to determine compression and shear wave velocities. Asexplained further below, the processor may process the dispersion curvemeasurements to derive at least formation shear velocity and acousticanisotropy. Alternatively, these measurements may be communicated to acontrol module or a surface processing facility to be combined there. Ineither case, the derived acoustic properties are associated with theposition of the logging tool to provide a formation property log. Anetwork interface 122 connects the acoustic logging tool to acontrol/telemetry module via a tool bus, thereby enabling the digitalsignal processor 102 to communicate information to the surface and toreceive commands from the surface (e.g., activating the tool or changingits operating parameters).

FIG. 6 is a block diagram of an illustrative surface processing systemsuitable for collecting, processing, and displaying logging data. Insome embodiments, a user may further interact with the system to sendcommand to the bottom hole assembly to adjust its operation in responseto the received data. The system of FIG. 6 may take the form of acomputer that includes a computer 50, a computer monitor 56, and one ormore input devices 54A, 54B. Located in the computer 50 may be a displayinterface 602, a peripheral interface 604, a bus 606, a processor 608, amemory 610, an information storage device 612, and a network interface614. Bus 606 interconnects the various elements of the computer andtransports their communications.

In examples, the surface telemetry transducers may be coupled to theprocessing system via a signal digitizer 38 and the network interface614 to enable the system to communicate with the bottom hole assembly.In accordance with user input received via peripheral interface 604 andprogram instructions from memory 610 and/or information storage device612, the processor processes the received telemetry information receivedvia network interface 614 to construct formation property logs anddisplay them to the user.

The processor 608, and hence the system as a whole, generally operatesin accordance with one or more programs stored on an information storagemedium (e.g., in information storage device 612 or information storagemedia 52 that may be removable). Similarly, the bottom hole assemblycontrol module and/or processor 102 operates in accordance with one ormore programs stored in an internal memory. One or more of theseprograms configures the tool controller, the bottomhole assembly controlmodule, and the surface processing system to individually orcollectively carry out at least one of the acoustic logging methodsdisclosed herein.

In examples, formation properties may utilize three parameters tocharacterize transversely isotropic materials. In terms of thecomponents of the elastic stiffness matrix, at least one of the threeparameters was defined as:

$\begin{matrix}{\gamma = \frac{c_{66} - c_{44}}{2C_{44}}} & (1)\end{matrix}$where, as an aside, we note that the stiffness constant C₄₄ equals theshear modulus for a vertically-traveling horizontally polarized shearwave, and stiffness constant C₆₆ equals the shear modulus for ahorizontally-traveling horizontally polarized shear wave. At timeshereafter, this parameter may be referred to as the shear waveanisotropy, or Thomsen gamma. A perfectly isotropic formation would haveγ=0, while many shale formations often have shear wave anisotropies onthe order of 20-30%. VTI information plays an important role in seismicimaging of reservoirs, thus it is desirable to obtain VTI information asa function of depth from acoustic logging tools. Such measurements canbe influenced by a variety of factors including mud speed, boreholerugosity, contact between the tool and the wall (“road noise”),formation inhomogeneity, mode contamination from off-centering, anddrilling noise.

In addition to VTI information, mud slowness may be a parameter that maybe useful to invert waveform sonic data for elastic anisotropy. Inexamples, mud slowness may be utilized in an inversion for the VTIanisotropy parameter, Thomsen Gamma and C₄₄, from Stoneley and flexuraldispersion curves given a known mud slowness. In examples, the inversionmay be sensitive to mud slowness, where an error of 1% to 5% in μs/ft.in the assumed mud slowness may result in the Thomsen Gamma inversionparameter being off by a factor of two.

During measurement operation of a wellbore, processing of a wellbore mayinvolve zoning in about 50 ft. to about 100 ft. (about 15 meters toabout 30 meters) sections, inverting for a global (i.e. depthindependent in a section) mud slowness in each section, fitting thezone-to-zone mud slowness to a smoothly varying continuous mud slownesscurve, and doing a final depth-to-depth Thomsen Gamma inversion over theentire well using the mud slowness curve. In various parts of thedocument, the terms zone, section, and depth interval are usedinterchangeably. FIGS. 7 and 8 show the result of this procedure for mudslowness throughout a wellbore of interest. FIG. 7 shows the ‘global’objective function for a depth interval as a function of mud slowness.The inversion for mud slowness in a zone (depth interval) is done byminimizing the ‘global’ objective function. Thus, the estimated mudslowness for the depth interval of FIG. 7 would be approximately 215μs/ft. as defined by the minimum of the objective function. The globalobjective function for a depth interval will be described in more detaillater.

FIG. 8 shows the fitting of a smoothly varying mud slowness curve to themud-slowness estimates from all the zones. Note in this example the datapoints are separated by approximately 100 ft., which would be the depthinterval for each zone. However, smaller zones may be necessary if themud slowness changes more rapidly. This can happen, for example, when amud pill is placed in the well.

It should be noted that mud density (ρm) may be a parameter used in theinversion above. In examples, mud density may be a constant valuemeasured by an operator from a sample taken from a mud-pit duringdrilling operations. As illustrated in FIG. 8, mud slowness changesthroughout the wellbore, and it is known that small changes in mudslowness may cause large changes in output anisotropy parameter (ThomsenGamma inversion). Thus, any error in a mud slowness inversion due toerror in assumed mud density taken by the operator may impact results.

FIG. 9 is a graph showing changes in mud density versus changes in mudslowness for the same oil-based mud with increasing barite content. Asgraphed, the changes in mud slowness may be accompanied by correspondingchanges in mud density and so the establishment of the mud density mayaffect the inversion process. FIGS. 10A-11B illustrate sensitivity ofThomsen Gamma inversion to accuracy of the mud density input. Thefigures show the inversion for Gamma anisotropy parameter in the uppersection of the well for both an operator's mud density measurement(FIGS. 10A-10B), and using a conservative estimation of mud densitychange due to the settling of the borehole fluid (FIGS. 11A-11B). Asillustrated, the wrong mud density in a Thomsen Gamma inversion mayproduce an error of about or more than 50%.

FIG. 12 illustrates workflow 1200 to reduce error by inverting over azone for global mud density in addition to inverting for global mudslowness and variable Gamma anisotropy, (γ, C₄₄). In this context globalmeans constant (depth independent) over the zone, where a zone is a setof at least one or usually more contiguous depths, as opposed to varyingfrom depth-to-depth within the zone like the anisotropy does. Thisworkflow assumes the availability of a pre-computed library 1202 ofdispersion curves, i.e., the expected slowness of a given acoustic wavemode generated by a specific acoustic tool as a function of frequencyfor a given set of formation parameters. The library (theoreticaldispersion curves) may be computed ‘on-the-fly’ if processing power issufficient. In examples, the model formation parameters include mudslowness (dtm), compressional wave slowness (dtc), vertical shear waveslowness (dts, abbreviated in the following equations as s), shear waveanisotropy (γ), borehole radius (r), formation density (ρ), and muddensity (ρ_(m)). The effect of the acoustic tool on the dispersioncurves is usually modeled adequately by an effective tool radiusdetermined through lab experiments or analysis of large quantities offield data. Once the constant tool radius is determined in this manner,the library is generated as a function of the formation parameterslisted above. It should be obvious to those skilled in the art that someacoustic tools may require more sophisticated tool modeling to generatethe library. A more realistic tool model may consist of several toolparameters that may themselves be dependent on the formation parameters.In either event, once these tool parameters have been determined throughexternal means, the library for a specific tool may be generated andaccessed through the formation parameters. With these seven formationparameters, a corresponding dispersion curve may be retrieved from apre-computed library 1202. A direct retrieval may be possible if theparameter values correspond precisely to the values of a precomputedcurve, but more often the system may employ some form of interpolationto derive the desired dispersion curve from the precomputed curves fornearby parameter values.

The workflow of FIG. 12 is as follows. First an initial estimated mudslowness and mud density is chosen for the zone (block 1216). Denotethem as dtm_(est) and ρ_(m,est). Further, acquire the formationparameters dts_(est), dtc, r, and ρ, from external sources, typicallylogs, for the depths in the zone. These parameters are depth dependentalthough for convenience the subscript, d, is not shown. dts_(est) is aninitial estimate of the shear slowness (C₄₄=ρ/(dts_(est))²) used tocenter the allowed inversion bounds for dts, i.e. the final inverted dtsvalue is assumed in the range [dts_(est)−DS, dts_(est)+DS].

Also compute the data dispersion curves, Sx^(d)(f), from the acousticwaveforms for the depths in the zone. The depth dependent parameters anddispersion curves are shown in block 1206. Denote the portion of the(possibly non-uniform) library parameter grid coordinates spanning(γ_(min), γ_(max)) and dts_(est)±DS as(γ_(n) ,s _(m))=(γ_(n−1) ,s _(m−1))+(Δγ_(n) ,Δs _(m))m=1,. . .,M−1;n=1,. . . ,N−1  (2)

(γ_(min), γ_(max)) and DS are additional constant parameters noted inblock 1216 defining the inversion grid in slowness and gamma. The gridresolution should be fine enough so that theoretical dispersion curvesoff the gamma, s grid may be accurately estimated by linear equations ingamma and s. As noted previously, the library dispersion curves areinterpolated onto the gamma, s grid at the values of the other formationparameters (dtm_(est), ρ_(m,est), dtc, r, and ρ). This is shown in block1204. The gamma, s grid defines a mesh of linear regions in any ofseveral possible ways, but for the sake of providing a concrete examplewe will define a triangular mesh with verticesΔ_(jnm)={(γ_(n+j) ,s _(m+j)),(γ_(n+1) ,s _(m)),(γ_(n) ,s_(m+1))},j=0,1;n=0,. . . ,N−2;m=0, . . . ,M−2  (3)The slowness of mode X within a triangle is expressible linearly asS _(X)(f,γ,s)=S _(x)(f,γ _(n+j) ,s _(m+j))+(γ−γ_(n+j))a _(X,jnm)+(s−s_(m+j))b _(X,jnm)(γ,s)∈Δ_(jnm)  (4)where the coefficients as a function of frequency are given by

$\begin{matrix}{{a_{X,{jnm}} = \frac{{S_{X}\left( {f,\gamma_{n + 1},s_{m + j}} \right)} - {S_{X}\left( {f,\gamma_{n},s_{m + j}} \right)}}{\Delta\gamma_{n + 1}}}{a_{X,{jnm}} = \frac{{S_{X}\left( {f,\gamma_{n + j},s_{m + 1}} \right)} - {S_{X}\left( {f,\gamma_{n + j},s_{m}} \right)}}{\Delta s_{m + 1}}}} & (5)\end{matrix}$and Sx(f, γ_(n), s_(m)) are the theoretical library dispersion curves onthe grid.

With this framework in place, we select an objective function (not theglobal objective function mentioned earlier) for the inversion algorithmto minimize with respect to γ and s at each depth in the zone. Theinversion corresponds to block 1210, the octagon. A suitable function isthe L2 norm:L2=Σ_(X,f)[S _(X)(f,γ,s)−S _(X) ^(d)(f)]² W _(x)(f)  (6)where W_(x)(f) is a frequency dependent weighting (computed in block1208 and described further below) and S_(x) ^(d)(f) is the dispersioncurve computed from the waveform data for acoustic wave propagation modeX at a given depth (usually X={flexural, Stoneley}, but other modes maybe used if they are sensitive to the inversion parameters).Differentiation and algebraic manipulation show that the anisotropy, γ,and shear wave slowness, s, that minimize the L2 norm are the solutionsto the following:

$\begin{matrix}{\mspace{20mu}{{{A\left\lfloor \begin{matrix}{\gamma - \gamma_{n}} \\{s - s_{m}}\end{matrix} \right\rfloor} = \begin{bmatrix}u_{\gamma} \\u_{s}\end{bmatrix}}\mspace{20mu}{where}}} & (7) \\{\mspace{20mu}{{A \equiv \left\lfloor \begin{matrix}{\sum_{X,f}{W_{X}a_{X,{jnm}}^{2}}} & {\sum_{X,f}{W_{X}a_{X,{jnm}}b_{X,{jnm}}}} \\{\sum_{X,f}{W_{X}a_{X,{jnm}}b_{X,{jnm}}}} & {\sum_{X,f}{W_{X}b_{X,{jnm}}^{2}}}\end{matrix}\  \right\rfloor}\mspace{20mu}{and}}} & (8) \\{\begin{bmatrix}u_{\gamma} \\u_{s}\end{bmatrix} \equiv {- \left\lfloor \begin{matrix}{\sum_{X,f}{W_{X}{a_{X,{jnm}}\left( {{S_{X}\left( {\gamma_{n + j},s_{m + j}} \right)} - S_{X}^{d}} \right)}}} \\{\sum_{X,f}{W_{X}{b_{X,{jnm}}\left( {{S_{X}\left( {\gamma_{n + j},s_{m + j}} \right)} - S_{X}^{d}} \right)}}}\end{matrix} \right\rfloor} \equiv {- \begin{bmatrix}{\sum_{X,f}{W_{X}a_{X,{jnm}}c_{X,{jnm}}}} \\{\sum_{X,f}{W_{X}b_{X,{jnm}}c_{X,{jnm}}}}\end{bmatrix}}} & (9)\end{matrix}$

For brevity, the frequency dependence of the variables in equations(8)-(9) has been suppressed. Note that other weighting-dependentobjective functions and inversion algorithms may alternatively be used.It is not necessary that the objective functions provide an analyticsolution. For example, the L1 norm could be used together with a simplexinversion algorithm.

A solution to equation (7) can be found for each mesh triangle. Thesolution that lies within the boundaries of the triangle giving rise toit will be the correct solution.(γ_(jnm) ,s _(jnm))∈Δ_(jnm)  (10)

In examples, it may be possible, due to numerical errors, that a correctsolution lying near the boundary might be calculated to be just outsidethe boundary, so this possibility should be accounted for. Thetheoretical dispersion curves generally change monotonically withrespect to (γ,s), so if the theoretical dispersion curves are a good fitto the data dispersion curves a single solution may be found via aniterative search. However, in the case of extremely noisy data or datathat does not match the theoretical dispersion curves (e.g., due toborehole breakout), multiple solutions may exist. In this situation, theinversion might average the solutions and take the locus of thesolutions as the uncertainty. Alternatively, the inversion might performan exhaustive search to identify the position in the (γ,s) parameterspace of the global minimum of the objective function as the solution.In either case, the result should be flagged as suspect due to poor dataquality.

Other possible reasons for the system being unable to determine asolution might include the correct solution being located outside thelibrary grid. In this case, pre-computed library 1202 may be expanded toinclude the necessary region. If the chosen acoustic modes all havesmall or uneven sensitivities to the anisotropy and slowness parameters,the a_(x,jnm) and/or b_(x,jnm) coefficients near the minimum may beextremely small, making the matrix in equation (7) ill-conditioned. Inthis case, different or additional modes should be included in theanalysis. In any event any solutions found are preferably flagged assuspect and ignored when doing the mud slowness, mud density inversiondescribed further below.

Though the foregoing example only interpolates over Thomsen coefficientand vertical shear, the equations may be extended in a straightforwardmanner to invert for other parameters as well. For example if there isno formation density available at this depth one could invert for it aswell. However, as the number of inverted parameters increases theproblem eventually becomes ill posed (non-unique solution). Furthermore,execution time will increase.

As previously indicated, using a noisy portion of the dispersion curvesto do the inversion may adversely affect the inversion process. Theeffect of noise may be reduced by associating a frequency-dependentweighting function with each of the acquired dispersion curves from thetool. This may be done if the set of theoretical curves used for a givendepth provide an estimate of what the shape of the dispersion curvescomputed from the data should look like if no noise were present. Usingthis a priori knowledge an estimate of what portions of the dispersioncurves computed from the data have substantial noise may be used tocompute a weighting function to dampen those frequencies. Forconvenience drop the subscripts on the triangle symbol, Δ. Define thefunction S_(X,Δ) ^(d) asS _(X,Δ) ^(d)(f)=S _(X) ^(d)(f)−S _(X,Δ)(f)  (11)where the function S_(X,Δ)(f) is the average of the theoreticaldispersion curves over the vertices of the triangle. The noise in theneighborhood, Df, of a given frequency is estimated for a triangle fromthe normalized variance,

$\begin{matrix}{{\sum_{X,\Delta}^{d}(f)} = {\frac{1}{N_{f}}{\sum_{f^{\prime} = {f - {Df}}}^{f^{\prime} = {f + {Df}}}\left\lbrack \frac{{S_{x\Delta}^{d}\left( f^{\prime} \right)} - {{\overset{¯}{S}}_{X,\Delta}(f)}}{S_{X,\Delta,{{MAX} -}}S_{X,\Delta,{MIN}}} \right\rbrack^{2}}}} & (12)\end{matrix}$

where S_(X,Δ,MAX) and S_(X,Δ, MIN) are the maximum and minimum slownessvalues over all frequencies of S_(X,Δ), and S_(X,Δ) ^(d) is the mean ofS_(X,Δ) ^(d) over the frequency band. The variance computed in equation(12) can be used to compute weights.

One illustrative embodiment employs the following weighting function:

$\begin{matrix}{{W_{X,\Delta}(f)} = \frac{\min\limits_{f}\left( \sqrt{\sum_{X,\Delta}^{d}(f)} \right)}{\sqrt{\sum_{X,\Delta}^{d}(f)}}} & (13)\end{matrix}$

This function gives the measured dispersion curve more weight where itsshape looks like the shape of the theoretical dispersion curves. If thevariance is low relative to other parts of the dispersion curve it willhave a relatively high weighting. If the dispersion curve drifts oroscillates wildly at low or high frequency due to poor SNR, theweighting is less.

One possible problem occurs if the dispersion curve drifts and thenflattens out at low or high frequency. Then the flat region would have asubstantial weight. This effect may be reduced by limiting the frequencyrange. Find the frequency, f_(max), corresponding to the maximum ofequation (13). Recompute equation (12) using S _(X,Δ)(f)=S_(X,Δ)(f_(max)) and normalize it. Denote the result as Σ_(X,MAX)^(d)(f). Then compute new weights, W′_(X,Δ)(f) by masking the weights ofequation (13) as follows:

$\begin{matrix}{{W_{X,\Delta}^{\prime}(f)} = \begin{Bmatrix}{W_{X,\Delta}(f)} & {{{for}\mspace{14mu} f_{1}} < f < f_{2}} \\0 & {otherwise}\end{Bmatrix}} & (14)\end{matrix}$where f₁ is the highest frequency less than f_(max) such that Σ_(X,MAX)^(d)(f)>W_(X,Δ)(f) and f₂ is the lowest frequency greater than f_(max)such that Σ_(X,MAX) ^(d)(f)>W_(X,Δ)(f). The low and high frequencyregions where the dispersion curves drift are suppressed. Regions withsmall ripple have higher weights as desired.

The weighting functions of equations (13) or (14) may be applied inequations (8)-(9) for each triangle, or an average over the triangles toget a single set of weights. In examples, the weights may be zeroed outwhen they fall below a threshold. Another alternative is to take then'th root of the weights after masking to flatten them. Otheralternatives may be readily conceived. Specifically, the set oftheoretical curves used for a given depth provide an estimate of whatthe shape of the dispersion curves computed from the data should looklike if no noise were present. Using this a priori knowledge an estimateof what portions of the dispersion curves computed from the data havesubstantial noise may be used to compute a weighting function to dampenthose frequencies.

Returning to FIG. 12, the inversion process for the depth intervalbegins in block 1206 and 1216 with the setting of the depth dependent(“at depth”) and global parameters respectively. In this context, inorder to avoid an ill-posed problem, the depth dependent parameters areconsidered “fixed” parameters with the exception of shear slownessdts_(est). Fixed parameters are independently measured depth dependentparameters such as formation density, ρ, compressional slowness, dtc,and borehole radius, r, that are considered known and not changed duringthe inversion. The initial shear slowness is considered accurate enoughto center the s, γ grid, but then both s and γ are inverted for asdescribed previously. As a Quality Control check, the final shear waveestimate may be compared to the original shear estimate. In a perfectworld they should be equal. If there is a large difference between themeither the initial estimate taken from an external source is wrong, orthe anisotropy inversion failed. The global parameters are independentof depth within the zone and may be inverted for, such as dtm_(est), andρ_(m,est), or not changed during the inversion (ΔS, γ_(min), γ_(max)).The limits on the range of anisotropy parameter values and shear waveslowness values are set based on the user's experience and expectations.Compressional wave slowness, dtc, and the initial shear wave estimate,are typically derived from acoustic waveform measurements using standardtechniques (e.g., measuring the arrival time of the compressional wavemode), while formation density, ρ, is usually taken from neutron densitylogs. Initial estimates of the drilling fluid (“mud”) slownessdtm_(est), and mud density, ρ_(m,est), may be made in any suitablefashion including the use of default values, mud pit measurements, userinput, or average values from previous acoustic logs in the region. Theinversion process obtains relevant dispersion curves, such as Stoneley,Flexural, and/or the like (block 1206). In block 1208, the weightfunction is determined, then in block 1210 the process jointly invertsthe dispersion curves at depth for shear wave slowness and anisotropyvalues. Block 1210 uses variables from blocks 1204, 1206, and 1208 and1216 and equations 7-10 or their equivalent. Block 1212 holds theinverted values for shear wave slowness and anisotropy for all depths inthe interval at fixed mud slowness and density. In block 1214, the mudslowness and mud density are inverted for by varying them to minimizethe global objective function (not to be confused with the globalminimum in a parameter space of an objective function) described next.

Referring again to FIG. 12, the operations of blocks 1204, 1206, 1208,and 1210 are repeated for each logging tool depth to obtain ananisotropy and slowness estimate for all the depths in the depthinterval. In block 1214, the inversion process updates an estimateddrilling fluid (“mud”) slowness dtm_(est), and mud density, ρ_(m,est),and computes a global objective function that uses all the depths, d, inthe zone, e.g., the sum of L2 norms over the zone depths evaluated atthe current values of the depth dependent values (γ(dtm_(est),ρ_(m,est)), s(dtm_(est), ρ_(m,est))). Dropping the est subscript forconvenience,L2(dtm,ρ)=Σ_(X,f,d)[S _(X)(f,γ _(d)(dtm,γ),s _(d)(dtm,γ),dtm,ρ)−S _(X)^(d)(f)]² W _(X,d)(f,dtm,ρ)  (15)

Here, the index d refers to depth, and S_(X) ^(d)(f) is the computeddispersion curve from waveforms at depth d. (The weights should benormalized across depths and mud slowness/density. Often the dependenceof the weights on mud slowness/density can be neglected, i.e., if asuitable set of weights that dampens the correct portions of the deriveddispersion curves is found for some mud slowness/density, the sameweights may be applied for other mud slowness/density values since thedata itself does not change.) This global (i.e. using all the depths inthe interval) objective function may be minimized with respect to mudslowness and mud density using a 2-D minimization algorithm. The outputis the estimated mud slowness, mud density, and depth dependent Thomsencoefficients and vertical shear slownesses for the zone as defined bythe position in the parameter space of the global objective functionsglobal minimum. It should be noted, the term ‘global’ is being used twoways. The ‘global objective function’ is the objective function ofequation (15) using all depths in a depth interval. The position of the‘global minimum’ in a parameter space of an objective function (whetherthe global objective function defined by equation (15) or the onedefined for a specific depth in equation (6)) defines the estimate ofthe parameters. An example global objective function is shown in FIG.13.

In examples, the inversion workflow in FIG. 12 may be done by bruteforce (i.e. computing the objective function shown in FIG. 13, over theentire slowness-density grid), which may increase the length of time tocompute the function. As illustrated in FIG. 14, in examples, a workflow1400 may reduce the computational burden. In step 1402 an operator mayset an interval for the wellbore and initialize mud slowness and muddensity. The interval may be any section within the wellbore that may bemeasured. In step 1402 the operator may set a mud density to anoperator's measurement of the mud density at a well site. In step 1404,the operator may invert for mud slowness with a fixed mud density, i.e.find the global minimum of the objective function described in equation15 along the line of fixed mud density. Then in step 1406, the operatormay invert for mud density with a fixed mud slowness starting at theminimizing point of the previous step, i.e. find the global minimum ofthe objective function described in equation 15 along the line of fixedmud slowness. The process 1404-1406 is repeated until the mudslowness/density at the objective function minimum along a line ofconstant mud slowness or density stops changing between iterations(decision block 1408). This signifies the global minimum of theobjective function has been reached and found the best estimate of muddensity and mud slowness for the depth interval. FIG. 15 illustrates atwo-step convergence result from workflow 1400. This entire process isrepeated for each depth interval (block 1410). Once the inverted mudslowness and mud density are determined for all zones, the mud slownessand mud density from all zones are fitted to smoothly varying continuouscurves as a function of depth (block 1412), and a final depth-to-depthdts, Thomsen Gamma inversion may be performed over the entire wellbore(block 1414). Alternatively, the order of blocks 1404 and 1406 may beswitched in the workflow.

An alternative method to fitting the mud slowness and mud density curvesas a function of depth may include performing a linear regressionanalysis on the inverted mud slowness and mud density results for allthe zones to determine a low order relationship between mud slowness anddensity as illustrated in FIG. 16, which shows a linear relationship.FIG. 16 illustrates a linear regression analysis, where the finalinversion over the well uses the mud curve and the regressionrelationship instead of the fitted mud and density curves.Alternatively, the final inversion uses the density curve and theregression relationship. As discussed above, the workflows invert forthe density and mud slowness. However, if the relationship between mudslowness and density may be established through other means (e.g. labdata), this relationship may be used to determine the correct trial muddensity, trial mud slowness pair and invert only for mud slowness (oronly for mud density).

Improvements from the workflows listed above may allow an operatordirect determination of borehole fluid density and mud slowness as afunction of depth using multi-mode analysis of full waveform sonic data.This improves inversion for horizontally-polarized, verticallypropagating shear slowness, dts, and Thomsen gamma anisotropy, γ, usingfull-waveform sonic data. Knowledge of mud density and mud slowness as afunction of depth will also improve any other algorithm that uses theseparameters.

Acoustic logging measurements may be valuable for determining thevelocity structure of subsurface formations, which information may beuseful for migrating seismic survey data to obtain accurate images ofthe subsurface formation structure. Subsurface formations may often beanisotropic, meaning that the acoustic wave's propagation speed dependson the direction in which the wave propagates. Most often theformations, even when anisotropic, may be isotropic in the horizontalplane. This version of anisotropy is defined as vertical transverseisotropy (VTI). Accurate imaging may account for such anisotropy duringthe migration process. Such imaging enables reservoirs to be delineatedfrom surrounding formations, and further indicates the presence offormation boundaries, laminations, and fractures, which information isdesired by an operator as they formulate a production strategy thatmaximizes the reservoir's economic value.

The preceding description provides various embodiments of systems andmethods of use which may contain different method steps and alternativecombinations of components. It should be understood that, althoughindividual embodiments may be discussed herein, the present disclosurecovers all combinations of the disclosed embodiments, including, withoutlimitation, the different component combinations, method stepcombinations, and properties of the system.

Statement 1: An acoustic logging method that may comprise acquiringwaveforms for multiple acoustic wave modes as a function of toolposition in a borehole; deriving position-dependent mode dispersioncurves from the waveforms; accessing a computed library of dispersioncurves for a vertical shear slowness (s) and a Thomsen gamma (γ) of agiven acoustic wave mode as a function of frequency; interpolatingdispersion curves in the computed library to an assumed knowncompressional wave slowness, a borehole radius, a formation density, amud density, and a mud slowness; computing an adaptive weight; andinverting dispersion curve modes jointly for a shear wave anisotropy, avertical shear wave slowness, an inverted mud slowness, and an invertedmud density as a function of depth.

Statement 2: The method of statement 1, wherein inverting joint modesfurther comprises: initializing the mud slowness and the mud density fora plurality of depths; minimizing an objective function to estimate γand s in at least one of the plurality of depths; computing a globalobjective function in the at least one of the plurality of depths; andvarying the mud slowness and the mud density and repeating the prior twosteps until the global objective function is minimized to obtain anestimated mud slowness and estimated mud density for the at least one ofthe plurality of depths.

Statement 3: The method of statement 2, repeating each step of claim 2for all depth intervals to generate the mud slowness and the mud densityfor each depth interval in the borehole.

Statement 4: The method of statements 1 or 2, wherein inverting jointmodes further comprises: creating a mud slowness curve and a mud densitycurve in view of depth for a well by fitting the mud slowness curve andthe mud density curve to the inverted mud slowness and the inverted muddensity.

Statement 5: The method of statements 1, 2, or 4, wherein invertingjoint modes further comprises: creating a mud slowness curve and a muddensity curve in view of depth for a well by fitting the mud slownesscurve and performing a regression analysis to create a relationshipbetween the mud slowness and the mud density using the inverted mudslowness and the inverted mud density.

Statement 6: The method of statements 1, 2, 4, or 5, wherein invertingjoint modes further comprises: creating a mud slowness curve and a muddensity curve in view of depth for a well by fitting a mud density curveand performing a regression analysis to create a relationship betweenthe mud slowness and the mud density using the inverted mud slowness andthe inverted mud density.

Statement 7: The method of statements 1, 2, or 4-6, wherein invertingjoint modes further comprises using the mud slowness and the mud densitycurves to invert at a plurality of depths in a well for a final Thomsengamma and the vertical shear slowness by minimizing a single depthobjective function at each depth in the borehole.

Statement 8: The method of statements 1, 2, or 4-7, further comprisingproducing a graph including the mud slowness against a depth of theborehole.

Statement 9: The method of statements 1, 2, or 4-8, further comprisingproducing a graph including the mud density against a depth of theborehole.

Statement 10: The method of statements 1, 2, or 4-9, wherein thecomputed library includes formation parameters of the mud slowness, thecompressional wave slowness, the vertical shear wave slowness, the shearwave anisotropy, the borehole radius, the formation density, and the muddensity.

Statement 11. An acoustic logging system that may comprise a loggingtool configured to be disposed in a borehole; a conveyance attached tothe logging tool, wherein the conveyance is configured to raise or lowerthe logging tool in the borehole; at least one sensor, wherein the atleast one sensor is disposed on the logging tool and configured toacquire waveforms; and at least one processor configured to: deriveposition-dependent mode dispersion curves from the waveforms; access acomputed library of dispersion curves for a vertical shear slowness (s)and a Thomsen gamma (γ) of a given acoustic wave mode as a function offrequency; interpolate dispersion curves in the computed library to anassumed known compressional wave slowness, a borehole radius, aformation density, a mud density, and a mud slowness; compute anadaptive weight; and invert dispersion curve modes jointly for a shearwave anisotropy, a vertical shear wave slowness, an inverted mudslowness, and an inverted mud density as a function of depth.

Statement 12. The system of statement 11, wherein the at least oneprocess is further configured to: initialize the mud slowness and themud density for a plurality of depths; minimize an objective function toestimate γ and s in at least one of the plurality of depths; compute aglobal objective function s in the least one of the plurality of depths;and vary the mud slowness and mud density and repeating the prior twosteps until the global objective function is minimized to obtain anestimated mud slowness and estimated mud density for the least one ofthe plurality of depths.

Statement 13. The system of statement 12, wherein the at least oneprocess is further configured to: repeat the steps of statement 12 forall depth intervals to generate the mud slowness and the mud density foreach depth interval in the borehole.

Statement 14. The system of statements 11 or 12, wherein the at leastone process is further configured to: create a mud slowness curve and amud density curve in view of depth for a well by fitting the mudslowness curve and the mud density curve to the inverted mud slownessand the inverted mud density.

Statement 15. The system of statements 11, 12 or 14, wherein the atleast one process is further configured to: create a mud slowness curveand a mud density curve in view of depth for a well by fitting the mudslowness curve and performing a regression analysis to create arelationship between the mud slowness and the mud density using theinverted mud slowness and the inverted mud density.

Statement 16. The system of statements 11, 12, 14, or 15, wherein the atleast one process is further configured to: create a mud slowness curveand a mud density curve in view of depth for a well by fitting a muddensity curve and performing a regression analysis to create arelationship between the mud slowness and the mud density using theinverted mud slowness and the inverted mud density.

Statement 17. The system of statements 11, 12, or 14-16, wherein the atleast one process is further configured to: use the mud slowness and themud density curves to invert at a plurality of depths in a well for afinal Thomsen gamma and the vertical shear slowness by minimizing asingle depth objective function at each depth in the well.

Statement 18. The system of statements 11, 12, or 14-17, wherein the atleast one process is further configured to: produce a graph includingthe mud slowness against a depth of a borehole.

Statement 19. The system of statements 11, 12, or 14-18, wherein the atleast one process is further configured to: produce a graph includingthe mud density against a depth of a borehole.

Statement 20. The system of statements 11, 12, or 14-19, wherein thecomputed library includes formation parameters of the mud slowness, thecompressional wave slowness, the vertical shear wave slowness, the shearwave anisotropy, a borehole radius, a formation density, and the muddensity.

It should be understood that the compositions and methods are describedin terms of “comprising,” “containing,” or “including” variouscomponents or steps, the compositions and methods can also “consistessentially of” or “consist of” the various components and steps.Moreover, the indefinite articles “a” or “an,” as used in the claims,are defined herein to mean one or more than one of the element that itintroduces.

Therefore, the present embodiments are well adapted to attain the endsand advantages mentioned as well as those that are inherent therein. Theparticular embodiments disclosed above are illustrative only, as thepresent disclosure may be modified and practiced in different butequivalent manners apparent to those skilled in the art having thebenefit of the teachings herein. Although individual embodiments arediscussed, the disclosure covers all combinations of all thoseembodiments. Furthermore, no limitations are intended to the details ofconstruction or design herein shown, other than as described in theclaims below. Also, the terms in the claims have their plain, ordinarymeaning unless otherwise explicitly and clearly defined by the patent.It is therefore evident that the particular illustrative embodimentsdisclosed above may be altered or modified and all such variations areconsidered within the scope and spirit of the present disclosure. Ifthere is any conflict in the usages of a word or term in thisspecification and one or more patent(s) or other documents that may beincorporated herein by reference, the definitions that are consistentwith this specification should be adopted.

What is claimed is:
 1. An acoustic logging method that comprises:acquiring waveforms for multiple acoustic wave modes as a function oftool position in a borehole; deriving position-dependent mode fordispersion curves from the waveforms; accessing a computed library ofthe dispersion curves for a vertical shear slowness (s) and a Thomsengamma (γ) of a given acoustic wave mode as a function of frequency;interpolating the dispersion curves in the computed library to anassumed known compressional wave slowness, a borehole radius, aformation density, a mud density, and a mud slowness; computing anadaptive weight; and inverting dispersion curve modes jointly for ashear wave anisotropy, a vertical shear wave slowness, an inverted mudslowness, and an inverted mud density as a function of a depth of theborehole.
 2. The method of claim 1, wherein said inverting dispersioncurve modes jointly further comprises steps: initializing the mudslowness and the mud density for a plurality of depths; minimizing anobjective function to estimate the γ and the s in at least one of theplurality of depths; computing a global objective function in the atleast one of the plurality of depths; and varying the mud slowness andthe mud density and repeating said initializing the mud slowness and themud density and said minimizing the objective function until the globalobjective function is minimized to obtain an estimated mud slowness andestimated mud density for the at least one of the plurality of depths.3. The method of claim 2, repeating the steps of claim 2 for all depthintervals to generate the mud slowness and the mud density for eachdepth interval of said all depth intervals in the borehole.
 4. Themethod of claim 1, wherein said inverting dispersion curve modes jointlyfurther comprises: creating a mud slowness curve and a mud density curvein view of the depth for the borehole by fitting the mud slowness curveand the mud density curve to the inverted mud slowness and the invertedmud density.
 5. The method of claim 1, wherein said inverting dispersioncurve modes jointly further comprises: creating a mud slowness curve anda mud density curve in view of the depth for the borehole by fitting themud slowness curve and performing a regression analysis to create arelationship between the mud slowness and the mud density using theinverted mud slowness and the inverted mud density.
 6. The method ofclaim 1, wherein said inverting dispersion curve modes jointly furthercomprises: creating a mud slowness curve and a mud density curve in viewof the depth for the borehole by fitting the mud density curve andperforming a regression analysis to create a relationship between themud slowness and the mud density using the inverted mud slowness and theinverted mud density.
 7. The method of claim 1, wherein said invertingdispersion curve modes jointly further comprises using the mud slownessand the mud density to invert at a plurality of depths in the boreholefor a final Thomsen gamma and the vertical shear slowness by minimizinga single depth objective function at each depth of the plurality ofdepths in the borehole.
 8. The method of claim 1, further comprisingproducing a graph including the mud slowness against the depth of theborehole.
 9. The method of claim 1, further comprising producing a graphincluding the mud density against the depth of the borehole.
 10. Themethod of claim 1, wherein the computed library includes formationparameters of the mud slowness, the compressional wave slowness, thevertical shear wave slowness, the shear wave anisotropy, the boreholeradius, the formation density, and the mud density.
 11. The method ofclaim 1, further comprising: triggering a monopole acoustic source,which is configured to produce an acoustic pressure wave; and recordingone or more pressure variations from the acoustic pressure wave with areceiver array.
 12. An acoustic logging system that comprises: a loggingtool configured to be disposed in a borehole; a conveyance attached tothe logging tool, wherein the conveyance is configured to raise or lowerthe logging tool in the borehole; at least one sensor, wherein the atleast one sensor is disposed on the logging tool and configured toacquire waveforms; and at least one processor configured to: deriveposition-dependent mode for dispersion curves from the waveforms; accessa computed library of the dispersion curves for a vertical shearslowness (s) and a Thomsen gamma (γ) of a given acoustic wave mode as afunction of frequency; interpolate the dispersion curves in the computedlibrary to an assumed known compressional wave slowness, a boreholeradius, a formation density, a mud density, and a mud slowness; computean adaptive weight; and invert dispersion curve modes jointly for ashear wave anisotropy, a vertical shear wave slowness, an inverted mudslowness, and an inverted mud density as a function of a depth of theborehole.
 13. The system of claim 12, wherein the at least one processis further configured to steps: initialize the mud slowness and the muddensity for a plurality of depths; minimize an objective function toestimate the γ and the s in at least one of the plurality of depths;compute a global objective function s in the least one of the pluralityof depths; and vary the mud slowness and mud density and repeating saidinitialize the mud slowness and the mud density and said minimize theobjective function until the global objective function is minimized toobtain an estimated mud slowness and estimated mud density for the leastone of the plurality of depths.
 14. The system of claim 12, wherein theat least one process is further configured to: repeat the steps of claim13 for all depth intervals to generate the mud slowness and the muddensity for each depth interval of said all depth intervals in theborehole.
 15. The system of claim 12, wherein the at least one processis further configured to: create a mud slowness curve and a mud densitycurve in view of the depth for the borehole by fitting the mud slownesscurve and the mud density curve to the inverted mud slowness and theinverted mud density.
 16. The system of claim 12, wherein the at leastone process is further configured to: create a mud slowness curve and amud density curve in view of the depth for the borehole by fitting themud slowness curve and performing a regression analysis to create arelationship between the mud slowness and the mud density using theinverted mud slowness and the inverted mud density.
 17. The system ofclaim 12, wherein the at least one process is further configured to:create a mud slowness curve and a mud density curve in view of the depthfor the borehole by fitting the mud density curve and performing aregression analysis to create a relationship between the mud slownessand the mud density using the inverted mud slowness and the inverted muddensity.
 18. The system of claim 12, wherein the at least one process isfurther configured to: use the mud slowness and the mud density toinvert at a plurality of depths in the borehole for a final Thomsengamma and the vertical shear slowness by minimizing a single depthobjective function at each depth of the plurality of depths in theborehole.
 19. The system of claim 12, wherein the at least one processis further configured to: produce a graph including the mud slownessagainst the depth of the borehole or the mud density against the depthof the borehole.
 20. The system of claim 12, wherein the computedlibrary includes formation parameters of the mud slowness, thecompressional wave slowness, the vertical shear wave slowness, the shearwave anisotropy, the borehole radius, the formation density, and the muddensity.